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PROBLEM TO BE SOLVED : To provide a short arc metal halide discharge lamp that has a high beam-condensing efficiency without using mercury and a good chromaticity and start-up luminous flux at the start and is easy in instantaneous restart, capable of dimming and hard to break the airtight container, and further has little fluctuation of its property, and a metal halide lamp lighting device and a head lamp. SOLUTION : The halide lamp comprises a fire resistant and light translucent airtight container 1 having an inner volume of 0.005-0.1 cc, a pair of electrodes 2, 2 having a distance of 6 mm or less between the electrodes, and a discharge medium filled in the airtight container containing the first halide composed of a halide containing at least sodium Na and scandium Sc, the second halide composed of a halide that has a relatively large vapor pressure and is made of a metal of one kind or plural kinds that does not easily emit light in the visible region compared with the metal of the first halide and is contained 1 mg or more per 1 cc of the inner volume of the airtight container, and a rare gas, but mercury is not filled essentially in the container.